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Journal of the Optical Society of America B

Effect of partial coherence on diffraction intensity of a Gaussian Schell-model beam using two-level atomic grating

Sobia Asghar, Ziauddin Ziauddin, Shahid Qamar, Sajid Qamar

Published Dec 13, 2016• 12 citations
Publisher

Abstract

The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.

DOI
10.1364/josab.34.000148

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The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.
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Partially coherent quantum-entangled beams combine quantum correlation with partial coherence, allowing them to maintain quantum characteristics while being more resistant to distortions caused by random media during propagation. In this study, we investigate the effect of coherence variation of such beams on non-local double-slit quantum interference. The spatial coherence variation is achieved by controlling the transverse coherence length of the Gaussian Schell model pump in the spontaneous parametric down conversion process. For a fixed beam size, the momentum correlation width of partially coherent biphotons increases with the decrease in the transverse coherence length. This results in a biphoton beam exhibiting multiple spatial modes, making it more suitable for studying the non-local features of quantum states in imaging, interference, and diffraction experiments. Our findings infer both high-quality and near-unity visibility of nonlocal interference using the partially coherent twin beams, even with the substantial decrease in the coherence of the pump. We believe these results can enhance robustness against the deleterious effects of the medium during propagation and can have potential applications in optical image cryptography, biomedical imaging, quantum lithography, and quantum holography.
We present a grating-based, single-shot method to estimate the transverse spatial coherence width δ\deltaδ of a partially coherent beam from a single far-field diffraction image. Building on closed-form far-zone grating theory \cite{Li2025FarZoneGrating}, we cast the measurement as a statistical inverse problem by combining a Gaussian Schell-model forward model with detector noise (Poisson shot noise and Gaussian read noise). A global likelihood-based fit of the full diffraction pattern yields δ^\hat{\delta}δ^ in one exposure, including regimes with significant diffraction-order overlap. We further derive Fisher information and the Cram\'er--Rao lower bound (CRLB) \cite{Kay1993} to predict achievable precision and to guide experimental design (choice of grating duty cycle and the number of diffraction orders used). At a peak level of ∼5×103\sim5\times10^3∼5×103 counts, Monte Carlo errors closely follow CRLB trends across a broad range of coherence widths.
We derive the spatial coherence and intensity profiles of beams emerging from two consecutive collimating apertures, and compare our results with data. We show how to make a Gaussian Schell-model (GSM) beam by assuming Gaussian apertures. Then we compare the intensity profile, the transverse coherence width and the divergence angle of a GSM beam with those same properties of a beam that is collimated with two hard-edged slits. The GSM beam formulae are simpler, and offer an intuitive way to understand how partially coherent beams interact with interferometers.
We propose a scheme for effectively creating a type of all optical device called electromagnetically induced two-dimensional grating by utilizing a four-level coherent atomic medium, which is coherently driven by two orthogonal standing-wave fields. With a far-off resonant trigger field, a spatially modulated cross-phase modulation takes place accompanied by vanishing absorption. The resulting phase grating can diffract the probe beam into high-order directions. When a resonant trigger field is applied on the atoms, the probe obtains gain without inversion due to the atomic coherence effect. And then a gain-phase grating is formed. The diffraction efficiency can be significantly improved compared with that of phase grating. The results show that the diffraction efficiencies attainable by the gratings strongly depend on the interaction length, coherent field intensity, probe field detuning and coherent field detuning. Therefore, the proposed gratings can be used as two-dimensional multi-channel beam splitter which have potential application in optical networking and communication.
The nonparaxial propagation of partially coherent Gaussian Schell-model (GSM) beams in a graded-index waveguide is studied using the coherent states and coherent modes decomposition methods, as well as perturbation theory. Long-scale decoherence and recoherence of the GSM beam occur due to the revival effect caused by mode interference. It is shown that the radius of coherence and the degree of coherence can be determined based on measurements of purely geometric characteristics of the GSM beam. The information entropy and quantum mechanical purity of GSM beams are evaluated.